Two-dimensional acoustic turbulence

Two-dimensional turbulence of the waves with linear dispersion law is analyzed numerically at small Mach numbers and large Reynolds numbers. It is shown that the energy-flux relation is close to E{∝}P2/3 as for a one-dimensional system. The analysis of the wave distribution in k space shows that the anisotropic large-scale pumping produces turbulence as a set of narrow jets that do not smear as the cascade proceeds towards high wave numbers. The energy spectrum along the direction of a jet is close to E(k_∥{){{∝}}k}_{{{∥}}}^{{{-}}2}due to shock waves, while the spectrum per unit interval of wave numbers is E(k)∝{P}2/3k^-1 contrary to all previous predictions. Probability density functions of the velocity and velocity differences are found and compared with recent theoretical predictions. {} 1996 The American Physical Society.